What is the integral from 5 to 7 of |f(4x)| ?

The integral from 5 to 7 of |f(4x)| is -48f

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integral from 5 to 7 of |f(4x)|

\int_{5}^{7} ∣ f (4 x) ∣ d x

- 48 f

Solution steps

\int_{5}^{7} ∣ f \cdot 4 x ∣ d x

Eliminate Absolutes

= \int_{5}^{7} - 4 f x d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - 4 f \cdot \int_{5}^{7} x d x

Apply the Power Rule

: [\frac{x ^{2}}{2}]_{5}^{7}

= - 4 f [\frac{x ^{2}}{2}]_{5}^{7}

Compute the boundaries:

12

= - 4 f \cdot 12

Simplify

= - 48 f

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What is the integral from 5 to 7 of |f(4x)| ?
The integral from 5 to 7 of |f(4x)| is -48f